Iterative Calculus of Voting Under Plurality

Abstract

We formalize a voting model for plurality elections that combines Iterative Voting and Calculus of Voting. Each iteration, autonomous agents simultaneously maximize the utility they expect from candidates. Agents are aware of neither other individuals’ preferences or choices, nor of the distribution of preferences. They know only of candidates’ latest vote shares and with that calculate expected rewards from each candidate, pondering the probability that voting for each would alter the election. We define the general form of those pivotal probabilities, then we derive efficient exact and approximated calculations. Lastly, we prove formally the model converges with asymptotically large electorates and show via simulations that it nearly always converges even with very few agents.